Question

What is the molar conductivity of $0.05\ \text{M}$ solution of sodium hydroxide, if its conductivity is $0.0118\ \text{S}\ \text{cm}^{-1}$ at $298\ \text{K}$?

• A. $236\ \text{S}\ \text{cm}^2\ \text{mol}^{-1}$
• B. $423\ \text{S}\ \text{cm}^2\ \text{mol}^{-1}$
• C. $354\ \text{S}\ \text{cm}^2\ \text{mol}^{-1}$
• D. $590\ \text{S}\ \text{cm}^2\ \text{mol}^{-1}$

Hint:

Dividing a value by $0.05$ is mathematically identical to multiplying that value directly by 20. Shifting your numerator to $11.8$ and multiplying by 20 ($11.8 \times 2 = 23.6$, then scaled by 10) gives $236$ instantly.

Answer 1

The Correct Option is A

Step 1: Understand the question.
A $0.05$ M NaOH solution has conductivity $\kappa = 0.0118$ S cm$^{-1}$. We must find its molar conductivity.

Step 2: Write the molar conductivity formula.
When $\kappa$ is in S cm$^{-1}$ and $c$ is in mol L$^{-1}$, we use:
\[ \Lambda_m = \frac{1000 \times \kappa}{c} \]

Step 3: Note the values.
$\kappa = 0.0118$ S cm$^{-1}$ and $c = 0.05$ mol L$^{-1}$.

Step 4: Put values in.
\[ \Lambda_m = \frac{1000 \times 0.0118}{0.05} = \frac{11.8}{0.05} \]

Step 5: Do the division.
Multiply top and bottom by 100 to clear the decimal.
\[ \Lambda_m = \frac{1180}{5} = 236\ \text{S cm}^2\ \text{mol}^{-1} \]

Step 6: Pick the answer.
The molar conductivity is $236$ S cm$^2$ mol$^{-1}$, which is option 1.
\[ \boxed{236\ \text{S cm}^2\ \text{mol}^{-1}} \]